Question

a. Explain how to create a synthetic portfolio to replicate a call option using Put-Call Parity. Discuss the practical implications of this synthetic call.

(3 mark)

b. Use equations and symbols to derive the net investment for this synthetic portfolio at initiation (Date 0).

                                                                                                                                                                 c. Use equations and symbols to derive the net positions of the portfolio at expiration (Date T) if (1) S_T < X  ; (2) S_T > X.  

Answer 1

A.

PUT-CALL PARITY

C= S+P-PV(K)

which means that you can create a synthetic call by buying put option, stock and selling a zero-coupon bond with PV(K).

Here,

S= stock price

P= Price of put

PV(K)= present value of a zero-coupon bond with a face value equal to strike price K.

Price of a European call is equal to the price of the stock and a put minus the price of a zero-coupon bond that matures on the exercise date of the option.

Practical Implications:

In order for put-call parity to work, there shouldn't be any transaction costs or taxes. In other words, the market should be a perfect market. Also, if we want to create a synthetic call of a specific strike price and maturity there should be available the put and zero-coupon with same strike price and maturity.

b.

C= S+P-PV(K)

c.

	S1>X	S1<X
Put PAYOFF	0	X-S1
Stock PAY OFF	S1	S1
Bond pay off	(X)	(X)
Net position	S-X	0

From the above table, you can see that the net payoff at the expiry is equal to the payoff of a call. Call pay off= Max(S-X, 0). It will have S-X if S>X and zero if S<X.